“The district in general, like anybody, was in shock, but at the same time we did not pass judgment,” West New York Superintendent John Fauta said yesterday.

The woman has not been charged with any crimes and remains at the Jersey City Medical Center undergoing psychological evaluation, an official with the Hudson County Prosecutor’s Office said yesterday, adding the investigation is ongoing.

The baby who was found by a parent as she was leaving the school about noon Friday was discovered to have “serious bodily injuries,” including a fractured skull, officials said.

The baby was first taken to Palisades Medical Center in North Bergen, but later Friday afternoon was airlifted to New York Presbyterian Hospital in Manhattan for specialized treatment, officials said.

Fauta said the woman has worked as a math teacher for special education students at the high school since 2007. She taught until April and then left on family leave and was not expected back until September, he said.

Fauta said any decision to change her job status will depend on the outcome of the Hudson County Prosecutor’s Office’s investigation.

Within an hour of leaving her baby girl at the school, the woman was taken into custody. She was stopped by Weehawken police for driving erratically on Boulevard East, officials said. According to sources, she said to officers during the stop, “I killed my baby.”

“Our concern is not only the child but also that the mother gets proper treatment,” Fauta said. “Being a parent myself, it brought a tear to my eye.”